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Bastian Rauch1, Raffaela Calabria2, Fabio Chiariello2, Patrick Le Clercq1, Patrizio Massoli2, Michael Rachner1 Accurate Analysis of Multicomponent-Fuel Spray Evaporation in Turbulent Flow Experiments in Fluids Vol. 52 (2012), pp.935-948 1 Institute of Combustion Technology (DLR), Stuttgart, Germany 2 Istituto Motori (CNR), Naples, Italy The original publication is available at www.springerlink.com http://dx.doi.org/10.1007/s00348-011-1169-0
The original publication is available at www.springerlink.com 1
http://dx.doi.org/10.1007/s00348-011-1169-0
Accurate Analysis of Multicomponent-Fuel Spray Evaporation in Turbulent Flow Bastian Rauch1, Raffaela Calabria2, Fabio Chiariello2, Patrick Le Clercq1,
Patrizio Massoli2, Michael Rachner1
1Institute of Combustion Technology, German Aerospace Center (DLR), Stuttgart, Germany +49 711 6862-210
+49 711 6862-578
www.dlr.de/vt/ 2Istituto Motori, Consiglio Nazionale delle Ricerche (CNR), Naples, Italy The aim of the paper is to perform an accurate analysis of the evaporation of single component and
binary mixture fuels sprays in a hot weakly turbulent pipe flow by means of experimental
measurement and numerical simulation. This gives a deeper insight into the relationship between
fuel composition and spray evaporation. The turbulence intensity in the test section is equal to
10%, the integral length scale is three orders of magnitude larger than the droplet size while the
turbulence microscale (Kolmogorov scales) is of same order as the droplet diameter. The spray
produced by means of a calibrated droplet generator was injected in a gas flow electrically
preheated. N-nonane, isopropanol and their mixtures were used in the tests. The generalized
scattering imaging technique was applied to simultaneously determine size, velocity and spatial
location of the droplets carried by the turbulent flow in the quartz tube. The spray evaporation was
computed using a Lagrangian particle solver coupled to a gas phase solver. Computations of spray
mean diameter and droplet size distributions at different locations along the pipe compare very
favorably with the measurement results. This combined research tool enabled further investigation
concerning the influencing parameters upon the evaporation process such as the turbulence,
droplet internal mixing and liquid phase thermophysical properties.
Spray Evaporation, Multiphase Flow, Spray Diagnostics, Numerical Simulation
The original publication is available at www.springerlink.com 2
http://dx.doi.org/10.1007/s00348-011-1169-0
Introduction
Environmental (IPCC 2007) and security of supply concerns cause an increase in
demand for alternative fuels in the transport and energy sectors. This push for a
change in fuel production pathways, especially for liquid fuels in the transport
sector can yield departures in the fuel composition hence in their thermophysical
properties with respect to well known and widely used refined petroleum based
fuels. Knowing that models and increasing computing power are available, in
design tools, one should shift from single component surrogate with constant
properties, to more realistic mixtures. Possibly, this should allow engine designers
to reach the optimum in terms of performance and nature-quantity of pollutants
under a wide range of fuel oxidation conditions.
Numerical simulation is an important tool for the design of new combustion
systems. Such design tools rely on validated sub-models, which themselves rely
on accurate experimental studies for their derivation and validation. Furthermore
by confronting numerical simulation with experimental data systematic
experimental errors can be detected and additional information about the physics
of the phenomena are accessible. This defines the overall investigation
methodology, which has enabled the accurate analysis of the multiphase-flow
under investigation.
When the fuel is supplied in liquid form it has to vaporize prior to burning.
Differences in liquid fuel composition can result in differences in local droplet
evaporation rate, liquid volume concentrations and vapor mass concentration
fields of reacting species and emissions (Le Clercq et al. 2010) in a combustion
chamber. Therefore, it is required to take into account the multicomponent nature
of the fuels to capture composition’s effects on the performance and emission of a
combustion system. Specifically, multicomponent-fuel droplet evaporation
models allow predicting accurately the times at which volatile components are
released in the gas phase. This is of importance when assessing threshold
operational situation like high-altitude relight or engine cold start (Caines et al.
2001; Mastorakos 2009).
The evaporation behavior of isolated pure species droplet (suspended) has been
extensively investigated (Birouk et al. 2006; Law 1982). Less data is available for
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the similar set-ups but using real fuels. Experimental studies concerning real fuel
sprays (monodisperse or polydisperse) with boundary conditions as accurately
defined as those for isolated droplet yet with more realistic surrounding
conditions, such as hot turbulent air flow, are limited (Ochs et al. 2001;
Sommerfeld and Qiu.1998).
The objective of the present paper is to study fuel spray evaporation of
multicomponent fuels in simplified yet semi-realistic conditions. Actually, the
conditions are simplified with respect to standard aero-engine operating
conditions, but with controlled boundary conditions to be able to perform accurate
computations. By utilizing experimental methods together with numerical
simulation it is aimed at gaining a detailed understanding of the investigated
phenomena and its influencing parameters. A generic experiment was built where
a monodisperse spray close to ambient temperature is injected into a preheated
weakly turbulent flow at ambient pressure. All boundary conditions required for
the computations were measured accurately. To characterize the spray evaporation
the generalized scattering imaging technique (Calabria et al. 2000) was applied to
simultaneously determine size, velocity and, spatial location of the evaporating
droplets. This technique has the advantage that it is weakly dependent upon the
refractive index; neglecting the refractive index for the droplet sizing yields a
measurement uncertainty smaller than 4% for the droplet sizing. Thus it is
possible to characterize fuels with complex composition hence unknown
thermophysical properties. The combination of experimental measurement and
numerical simulation is used to assess the capability of the combined methods in
resolving differences in the spray evaporation due to changes in the composition
of the fuels. Moreover, the numerical simulation was used to assess the influence
of turbulence, droplet internal mixing and the relative importance of the different
thermophysical properties responsible for the penetration length under the present
conditions.
Experimental system
An experimental system was developed to perform accurate measurements of
droplet/spray evaporation. The experimental link provides full optical access
thereby allowing different kinds of measurement techniques to be employed
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(Rauch et al. 2010). All inflow, outflow, and wall boundary conditions as well as
continuous flow and droplet initial conditions required for performing numerical
simulations and for validating droplet/spray evaporation models are determined
meticulously.
Fig. 1 a) is a schematic representation of the experimental system with the
measurement techniques employed. Fig. 1 b) shows in detail the flow
conditioning system and the position of the droplet generator. The flow field in
the test track is generated by two interacting flows; a preheated weakly turbulent
primary flow and a quasi-laminar secondary flow carrying the droplets. Droplets
are injected collinearly to the cold secondary gas flow direction. To control inflow
conditions especially ensure axisymmetry and generate the turbulence, a
combination of honeycombs and perforated plate (hole diameter 1.5 mm, open
surface factor 21%) are used. In the present configuration, flow velocities of up to
3 m/s at a maximum inlet temperature of 800 K can be reached.
The vibrating orifice aerosol generator (VOAG), Model 3450 of the TSI
Corporation, MN, USA, generates a monodisperse stream of droplets.
Interchangeable orifices allow varying droplets initial diameter from 21 µm to a
maximum of about 400 µm. Then, applying a transversal airflow and forcing the
stream through a cone-shaped hole disperses the droplets and generates the
monodisperse spray.
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Fig 1 Experimental system with a) applied measurement techniques and b) Inlet system: flow
conditioner and droplet generator
Both measurement techniques, the generalized scattering imaging (GSI) for spray
characterization and the particle image velocimetry (PIV) for velocity field, were
employed in the same experimental set up. In GSI configuration the CCD camera
was placed at a scattering angle ϑ=60°, where droplets size measurements exhibit
the minimum sensitivity to the refractive index. The camera was moved at an
angle ϑ=90° for PIV measurements. The generalized scattering imaging technique
(Calabria et al. 2000) is used to measure droplet diameter and droplet velocity.
GSI is a 2D light scattering sizing technique based on the properties of out-of-
focus images of droplets captured at a scattering angle of 60°. This technique has
the advantage that it is weakly dependent upon the refractive index; neglecting the
refractive index the measurement uncertainty is smaller than 4% for droplet
sizing. In case the refractive index of the liquid is known the measurement
uncertainty can be reduced to less than 1%. The droplet velocity is inferred from
correlating the droplet movement between two laser pulses on two different
frames.
The laser is a CFR200 Pulsed Nd:YAG Laser from the company Big Sky Laser
Technologies Inc. It has a wavelength of 532 nm, pulse duration of 8 ns and,
repetition rate of 15-30 Hz. The images are taken with the TSI Power View 4MP.
The camera has a high resolution with 4 million pixels (resolution 2048 x
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2048 px), it has a 12 bit intensity dynamic range and an image capturing rate of 16
frames per second. Variable exposure times and a protective mask are also part of
the camera features.
A J-type thermocouple is used for the characterization of the flow temperature
field. A fine grid of temperature measurement points was used close to the
secondary flow outlet, in the droplet evaporation onset region. In addition, the
temperature along the centerline of the secondary flow system was measured,
starting from the droplet generator to the secondary flow outlet (i.e.: main flow
tube inlet). To complete the set of accurate boundary conditions for the flow field
computation, the temperature distribution along the pipe wall and the temperature
of the secondary flow system were measured.
Computation
Spray transport, dispersion and, evaporation processes are computed using the
DLR in-house code SPRAYSIM (Le Clercq et al. 2009). It is a simulation tool
written in FORTRAN 95 developed at the German Aerospace Center, Institute of
Combustion Technology, for spray systems found in premixing/pre-vaporizing
modules and gas turbine combustors. SPRAYSIM can generate spray initial
conditions based on some state-of-the-art atomization models or fitting of
practical sprays initial conditions. Then, it performs the tracking of those
generated numerical particles in a Lagrangian framework on unstructured grids
and in steady or unsteady gasfields. In the particle’s momentum equation the drag
force as well as gravity is accounted for. Turbulent particle dispersion is modeled
in the present investigation by Blümcke’s spectral dispersion model (Blümcke et
al. 1993). Simpler dispersion models of Gosman-Ioannides-type are also
selectable. The liquid phase can consist of an arbitrary number of discrete and/or
continuous (PDF) species. The multicomponent heating and evaporation model is
an extension of the single component evaporation model of Abramzon and
Sirignano [2]. In the present study single-component droplets of n-nonane and
isopropanol as well as their binary (discrete) mixture were simulated. The
temperature distribution inside the liquid droplet can be treated in SPRAYSIM
either by a uniform temperature model or the conduction limit model or the
effective conductivity model of Abramzon and Sirignano (Abramzon et al. 1988).
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Concentration gradients inside the liquid droplet are not accounted for as the rapid
mixing model was used here. The system of ordinary differential equations is
solved simultaneously for each particle by an Adams-predictor-corrector scheme
with automatic internal stepsize control. SPRAYSIM can be used stand-alone or
coupled with different gas flow solvers. The data exchange happens by subroutine
calls from the gas flow solver or via files. Due to the high dilution rate of the
multiphase flow under investigation here SPRAYSIM was used stand-alone. The
carrier gas field was computed with the commercial CFD-code ANSYS® CFX-
12.0. Computational results based on a two-way coupling approach (not shown
here) displayed no differences with respect to the one-way coupling computations
presented in this paper.
The gas field CFD code solves the Reynolds-Averaged Navier-Stokes (RANS)
equations in their conservative form augmented with a transport equation for the
specific enthalpy. Additional transport equations for the gaseous species including
fuel vapor, for the turbulent kinetic energy and for the turbulent frequency are also
solved. Actually, the k-ω based shear-stress transport (SST) model of Menter
(Menter 1994) is used to close the Reynolds stress tensor based on the eddy
dissipation concept.
Boundary conditions
Experiments were performed using a 50 µm orifice and a liquid volume flow rate
of 0.59 cm³/min resulting in a calibrated droplet sprays with a modal value for the
diameter between 100 µm and 110 µm. The variation is due to the adjustment of
the frequency of the piezoelectric head, which was necessary to guarantee the
most stable conditions of operation of the droplet generator. The frequency had to
be adjusted for each given liquid and was in the range of 15 to 18 kHz.
The computational domain is shown in Fig. 2. The flow field boundary conditions
are summarized in Table 1 and described in more detail in Rauch et al. 2010.
These were kept constant for all measurements. The coordinate system is located
at the beginning and on the centerline of the experimental link. This is the first
position where measurements could be performed. Droplets and dispersion-air are
injected at [0,0,-131] (dimensions are in mm) in the direction of the z-axis.
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Y
Z
X
Inlet:Primary air
InletSecondary air
Exp
erim
enta
llin
kw
all
Outlet
Inle
tsys
tem
wal
l
Droplet inlet[ 0,0,-131 ]
r
z
Fig. 2 Computational domain
Boundary conditions Hot flow Inlet system wall -131 mm <z< -63 mm [K]
-63 mm <z< -5 mm [K] -5 mm <z< 0 mm [K]
345 373 873 723
Exp. link wall Constant temperature [K]: 363 Primary air inlet Mass flow [kg/s]
Temperature Turbulence intensity
0.983x10-3 Fig. 3 10%
Secondary air inlet Mass flow [kg/s] Constant temperature [K] Turbulence intensity
5.3584x10-5 365 1%
Droplet dispersion air
Mass flow [kg/s] Constant temperature [K] Turbulence intensity
2.95x10-5
300 1%
Table 1 Flow field boundary conditions
Results
Tests have been carried out for one set of flow conditions: mean velocity of 1.5
m/s and flow inlet temperature of 700 K. N-nonane, isopropanol and their
mixtures were used in the tests. The flow field computation results are validated
against PIV measurements. Then, spray evaporation computations are performed
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in a pre-computed flow field (one-way coupling) and compared to the spray
characteristics measurements.
Flow field validation
In order to recover a quasi-symmetrical flow field in the test section, a complex
flow conditioner was developed, which uses, amongst others, a porous medium
layer with a pore size of 25 µm. Smoke particles from incense sticks were used as
seeding material for the PIV measurements. These measurements have been
performed by seeding the droplet co-flow (secondary flow) forcing thereby the
seeds to pass through the flow conditioner. The smoke particle did not clog the
flow conditioner however they could only be used for measurements at room
temperature. Thus, the velocity field of the cold flow case was used for the
validation of the gas velocity field computations (Rauch et al. 2010) (not shown
here). Downstream the incoming laminar secondary (jet) flow (z=[100, 250 mm]),
the turbulence intensity was measured to be 10%. Hot flow field computations are
validated against the measured temperature field and are shown in the following.
z [mm]
T[K
]
-100 0 100 200 300 400 500 600300
400
500
600
700
Experimental dataComputation
r [mm]
z[m
m]
-50 0 50
-100
-50
0
50
100
150
200
250
300
350
T [K]
700650600550500450400350300
r [mm]
z[m
m]
-50 0 50
-100
-50
0
50
100
150
200
250
300
350
T [K]
700650600550500450400350300
(a) (b)
(c)
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Fig. 3 Hot flow temperature field without spray, (a) experimental data, (b) computation, (c)
temperature along the centerline
The computed temperature field displayed in Fig. 3 (b) is in good agreement with
the experimental measurement shown in Fig. 3 (a). In Fig. 3 (c), the computed
centerline temperature displays a slower temperature increase after z = 0 mm with
respect to the measurements. This can be explained by the enhanced heat transfer
from the surrounding hot primary airflow towards the center due to the transition
to turbulence. The computation shows a decline of the temperature rise instead.
This is in accordance with the findings from the cold flow simulation (Rauch et
al. 2010). In the computations, the transition to turbulence is delayed and less
spatially concentrated with respect to the experiment. In addition, a known
weakness of turbulence models based on two transport equations (k-ω for
example) is the underestimate of scalar mixing (e.g. temperature field). This
explains the weaker heat transfer in the vicinity of axis position z=0 mm observed
in the computation (Fig. 3 c).
Spray analysis: experimental data
Droplet evaporation measurements have been performed with the pure liquid fuels
n-nonane and isopropanol, and their binary mixtures with 30/70% and, 70/30% by
volume ratios.
Spray structure
First, the overall spatial distribution of the spray and its variation along the path
are analyzed. To this aim, the size and position of each droplet in the spray at
different axial positions were inferred from using the GSI laser diagnostic
technique. Fig. 4 shows the reconstruction of the spray spatial distribution for
fuels by GSI data in house developed post-processing. Measurements were
performed with a 25 mm step along the z axis, with the initial location centered at
z = 5 mm, then going down the axis all the way to z= 230 mm. Each captured
droplet is represented by a circle the diameter of which is proportional to its actual
size. The height of the spray section in every location is limited by the laser sheet
width and is equal to 10 mm. This post-processing method and associated
graphical representation allows verifying the centering and the tilting of the spray
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with respect to the quartz tube axis. During the tests, the maximum off-center
position and tilting were limited to 2 mm and 0.5°, respectively.
Fig. 4 Droplets size and position distributions after spray reconstruction for (a) n-nonane; (b) 30%
isopropanol / 70% n-nonane; (c) 70% isopropanol / 30% n-nonane; (d) isopropanol. Each
individual droplet is represented by a circle with a diameter proportional to the droplet size
From the plots displayed in Fig. 4, one can see that n-nonane is evaporating faster
than isopropanol although isopropanol has a lower boiling point and liquid heat
capacity with respect to the one of n-nonane. An explanation to this behavior will
be given in the last section of this chapter (Influencing parameters) by means of
the results of the numerical simulation.
Mean diameter evolution
From the repeated instantaneous measurements at different axial positions (see
Fig. 4), one can derive statistics about the droplet size distribution. On average,
500 droplets have been processed in each measurement position. The spatial
evolution of the droplet diameter ensemble average (mean of the distribution) and
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
D [µm]
1201101009080706050403020100
(a) (b) (c) (d)
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
D [µm]
1201101009080706050403020100
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
r [mm]
z[m
m]
-20 0 20
0
50
100
150
200
250
D [µm]
1201101009080706050403020100
(a) (b) (c) (d)
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z [mm]
D[µ
m]
50 100 150 2000
25
50
75
100
125
z [mm]
D[µ
m]
50 100 150 2000
25
50
75
100
125
z [mm]
D[µ
m]
50 100 150 2000
25
50
75
100
125
z [mm]
D[µ
m]
50 100 150 2000
25
50
75
100
125
MeanMean (filtered)std. dev.std. dev. (filtered)
(a) (b) (c) (d)
its standard deviation about the mean for the pure fuels and mixtures listed above
are given in Fig. 5. Isopropanol droplets (see Fig. 5 d) display the longest
evaporation distance. The deviation of droplet diameter distribution from the
mean is largest for n-nonane droplets while it is the smallest for isopropanol
droplets. The binary component mixtures behave similarly as the pure species,
which is in highest concentration.
Fig. 5 Droplet diameter dispersion, mean diameter and standard deviation for (a) n-nonane; (b)
30% isopropanol / 70% n-nonane; (c) 70% isopropanol / 30% n-nonane; (d) isopropanol
Some smaller and bigger droplets outside the normal range of droplet diameters
can be observed for all discrete distributions shown in Fig. 5. These can be due to
single random effects such as droplet coalescence, to droplet flight paths in the
secondary flow that are closer to the near wall hot region, or to droplet generator
instabilities (production of satellite droplets), which can result in the production of
satellite droplets. For the comparison with the computation these extreme values
have been filtered out.
D [µm]
Freq
uenc
y[-]
25 50 75 100 125 1500
0.1
0.2z = 5 (exp.)
Lower limit Upper limit
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Fig. 6 Diameter distribution and distribution limits identified by the filter at z = 5 mm
Since for the measurements a monodisperse spray is used, the diameter
distribution is monomodal. The additional modes which can be seen in Fig. 6 for
lower and high diameter ranges are due to random effects. To filter the data the
main peak of the distribution function is identified. Starting from this point the
two minimum values (threshold value: 0.002) in the distribution function, one for
the smaller diameters and one for the bigger diameters are identified. Droplets
outside this range are removed for the further data analysis.
Moreover, it should be emphasized that the laser sheet width, which is equal to 10
mm in the axial direction, adds substantially to the size distribution deviation
about the mean. Actually, Fig. 7 gives the relevant details concerning the droplet
size distributions within the upper and lower halves of the laser sheet separately.
As can be seen in Fig. 7 (a), at z = 80 mm the n-nonane droplet size distribution in
the upper half of the sheet (i.e.: earlier in the droplet lifetime with respect to the
middle of the sheet width, see Fig. 7 (b) has a bigger mean value than the
distribution in the lower half (i.e.: later in the droplet lifetime). This effect is more
pronounced for droplets that vaporize rapidly.
D [µm]
Freq
uenc
y[-]
0 50 1000
0.05
0.1
0.15
0.2 UpperLower
(a)
Laser sheet
Upper half
Lower half
(b)
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Fig. 7 Effect of averaging over the laser sheet. (a) sketch of the measurement volume; (b) Size
distribution of n-nonane droplets at z= 80 mm measured in the upper half and lower half regions of
the laser sheet
The second effect which has to be analyzed is the uncertainty in the droplet
diameter determination due to the laser sheet thickness. In GSI, the size of a
droplet is determined by measuring the spacing of the scattering oscillation in out-
of-focus images (Calabria and Massoli 2000). In the present configuration, the
defocus distance was equal 25 mm. However, droplets traversing the beam in
different locations will be subject to different magnifications. The laser sheet
thickness was 500 µm to allow high droplet detection rate. Considering, in first
order, a linear effect of the defocusing distance on the image magnification, the
expected uncertainty in the size determination due to the laser beam thickness is
about 2%. This uncertainty tends to broaden the size distribution toward both
extremes.
Finally, the influence of the droplet motion during the image acquisition
(exposure time) on the measurement accuracy has been also evaluated. In the
present case, the images were frozen by the short duration of the laser pulse. By
considering the laser pulse duration, 8 ns, and the maximum droplet velocity, 3
m/s, the maximum droplet’s shift during the image acquisition is equal to 24 nm.
Therefore, the maximum deformation of the droplet image is well within the one
pixel resolution of the digital system where 1px corresponds to approximately 10
µm. Thus, the finite duration of the laser pulse had negligible influence on the size
determination.
Droplet velocities
In addition to the droplet diameter and droplet position, the GSI technique enables
simultaneous measurements of droplet velocities. In Fig. 8, one can see the n-
nonane droplet velocity field within the laser sheet, which was centered here at the
location z = 5 mm. The main direction of the droplet velocity vector is collinear to
the z-axis.
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r [mm]
z[m
m]
-4 -2 0 2 4
0
2
4
6
8
10
velocity [m/s]3.22.82.421.61.20.80.40
Fig. 8 N-nonane, droplet velocities at z = 5 mm
For the analysis it is assumed that the flow is axisymmetric to the centerline. The
primary flow conditioner was designed to create a homogeneous inflow profile
without any radial or tangential velocity components. The honeycombs being part
of the system are 13 mm thick and have a characteristic size of 1 mm, thus any
other velocity component except the axial velocity is removed. This is supported
by the results of the mean radial droplet velocity shown in Fig. 9. Since the mean
value is close to zero, the single droplet radial velocities are due to the turbulent
dispersion.
z [mm]
radi
alve
loci
ty[m
/s]
0 50 100 150 200-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
N-nonane
Fig. 9 Plane averaged radial droplet velocity
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D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 5 mm
D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 30 mm
D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 55 mm
D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 80 mm
D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 105 mm
D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 105 mm
D [µm]
velo
city
[m/s
]
0 25 50 75 1000123
z = 155 mm
Additionally, Fig. 10 displays the droplet diameter as a function of the droplet
velocity at different measurement locations. The initial 30 mm are characterized
by a narrow droplet size distribution (around the mean D=100 µm) with a
relatively wide range of velocities [1.2 - 3.2 m/s]. There, the cloud of points in the
plot (Fig. 10, z= 30 mm) is mostly vertical. This is due to the larger gradients in
the gas flow velocity field (primary-secondary flows mixing layer) with respect to
the more uniform downstream region. Downstream, starting at around z= 55 mm
(see Fig. 10) although the droplet size distribution is substantially wider than in
the upstream region [z=5 - 30 mm], one observes a narrower velocity distribution
with respect to the upstream region.
Fig. 10 N-nonane: velocity diameter dependency at the different measurements locations
The Stokes number St (St = τd/τF) is the ratio of droplet relaxation time
τd (τd =ρLD2/18µg) and the convective flow characteristic time τF (τF=v/z), where v
is the mean flow field velocity and z is a characteristic dimension, in our case the
travel length of the droplet. The Stokes number was found to be always below
0.05 in test track, consequently the droplets will adapt rapidly to changes in the
mean flow.
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Spray analysis: numerical simulation
Spray initial conditions
To compute the evaporation of the fuel spray, the experimental size distribution
and volume concentration profiles at z=5mm were used as initial conditions for
the SPRAYSIM numerical code. Fig. 11 and Fig. 12 show the initial conditions data
extracted from the experiment for n-nonane droplets.
Droplets were injected at the first measurement position, z = 5 mm, in the
experimentally observed off-center position (-1.9 mm) and with the measured
spray radius (2.1 mm). It was assumed that the spray cloud is spherical symmetric.
The droplet temperature and initial composition (in the case of binary mixtures)
were estimated by performing computations of the spray heating-up behavior in
the secondary flow section before the test track. The droplet initial velocity
distribution was computed by taking into account the measured mean velocity and
its standard deviation.
r [mm]
φ/φ g
es[-]
-2 -1 0 1 20
0.05
0.1
Fig. 11 Initial diameter distribution
for n-nonane injection at z = 5 mm
Histogram comparison
In Fig. 13, the computed histograms for each measurement position are compared
with experimental data for n-nonane droplets. The agreement concerning the
shape of droplet diameters histograms is very good. In details, one can see that the
mean and the width of the computed size distributions agree very well with the
measurements. The development of multi-peaked distributions is also
qualitatively well captured for axial position below z=55 mm.
Fig. 12 Volume concentration
profile for n-nonane injection at
z = 5 mm
The original publication is available at www.springerlink.com 18
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Fig. 13 N-nonane diameter histogram at each measurement position. (a) experimental data, (b)
computations
(a) (b)
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http://dx.doi.org/10.1007/s00348-011-1169-0
In the computations, a slight shift toward smaller diameters occurs between
55 mm and 80 mm with respect to the experimental data. This is even more
pronounced after z = 130 mm. The same changes can be seen for the droplet mean
velocities (not shown). Further investigations have shown that the droplet co-flow
(secondary flow and dispersion air flow see Fig. 1b)) is subject to inlet pressure
variations. These fluctuations can have a direct influence on the droplet velocities.
The settings used in the actual GSI measurements were not changed during the
experimentation. They were tuned to resolve the droplet diameter with high
accuracy for most of the droplet lifetime (20 µm < D < 150 µm). The lower
detection limit of 20 µm can be seen in Fig. 13 a) for z = 130 mm and 155 mm.
Comparison of mean diameter evolution
Fig. 14 shows the comparison between the computed and measured mean
diameter spatial evolution in the flow direction. Table 2 reports the statistics of the
difference from the computed mean diameter to the experimental data. The
reported data represent for each fuel the differences averaged over all positions
with rejection of the last two. For the statistics the last two measurement
positions have been excluded since at these positions the droplets having a
diameter below 20 µm are not detected by the experimental system, but are
representing a considerable fraction of the droplet distribution. Hence the
experimental probability distribution function of the diameters measurement error
is too affected by the experimental procedure to provide data for a useful
comparison.
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Fig. 14 Comparison of computed and experimental arithmetic mean diameter for (a) n-nonane; (b)
isopropanol; (c) 30% isopropanol / 70% n-nonane; (d) 70% isopropanol / 30% n-nonane
One can see that both the mean diameter and the slope of the curves from the
computation results are in very good agreement with the measurements. For n-
nonane and the binary mixtures the agreement with experimental results is
excellent with a difference below 5%. The change in the slope at z = 80 mm for
the 30% isopropanol / 70% n-nonane mixture indicating a volatility-based
evaporation process (as opposed to frozen composition) is also very well
predicted by the computation. The isopropanol computation shows a good
agreement with respect to the experimental data. The predicted droplet diameter
toward the end of the penetration length for all fuels is equal to the measured
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120ExperimentComputationStd. dev. (exp.)Std. dev. (comp.)
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120ExperimentComputationStd. dev. (exp.)Std. dev. (comp.)
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120ExperimentComputationStd. dev. (exp.)Std. dev. (comp.)
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120ExperimentComputationStd. dev. (exp.)Std. dev. (comp.)
(a) (b)
(c) (d)
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value. As mentioned previously, after z = 55 mm the measured diameters of n-
nonane droplets are shifted toward higher values.
Fuel Mean difference [%] Minimum [%] Maximum [%]
N-Nonane 2.6 0.3 6.5
70% N-Nonane
30% Isopropanol
4.6 1.1 11.5
30% N-Nonane
70% Isopropanol
3.2 1.1 7.0
Isopropanol 8.2 1.0 17.4
Table 2 Difference of computed results with respect to experimental data excluding the last two
measurement positions
Influencing parameters
Additional computations have been performed to investigate the influencing
parameters on multicomponent-fuel evaporation process and to understand why n-
nonane droplets evaporate faster than isopropanol droplets (see Fig. 4, Fig. 5 and,
Fig. 14). Actually, the effect of turbulence, the influence of internal mixing on the
binary mixture fuels evaporation and finally the influence of the thermophysical
properties have been studied.
The flow field used for the experiments is characterized by a Reynolds Number of
900. An integral length scale of l ~ 10-1 m was estimated by using l=0.7r1/2 (Pope
2000) which is much larger than the droplet size (D=10-4 m) and suggests a minor
influence on the droplet evaporation (Wu et al 2001). Fig. 15 shows the
comparison of the evaporation of n-nonane in a laminar flow field and in the
present turbulent flow field. The difference is small and noticeable only past the
axis position z=70 mm, which corresponds to the shear layer development
between primary and secondary flows hence to the highest turbulence intensity
region (here 10%). This difference is comparable to the results of Wu et al 2001.
Moreover, since the turbulence integral length scale is three orders of magnitude
bigger with respect to the droplet initial diameter it is not the energy-containing
turbulent structures which interact with the droplets. Here, droplets are of
comparable sizes as the small dissipative structures, which are characterized by
The original publication is available at www.springerlink.com 22
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the Kolmogorov length scale. This translates into a turbulent Stokes number close
to unity when adopting the time scale perspective. Thus, for the present flow
conditions and liquid properties, we can formulate that weakly turbulent flows
have an impact on droplet evaporation when along their trajectory they encounter
region of comparable time and length scales as the small turbulence time and
length scales.
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120
Turbulent flow fieldLaminar flow field
Fig. 15 Comparison of mean diameter evolution for laminar and turbulent flow field conditions.
The model used is in this study is the rapid mixing model where temperature and
concentration gradients within the liquid phase are not resolved. To understand
the effect of liquid phase mixing, the two limiting cases were used in additional
computations, the results of which are presented here after. First, the frozen limit
(droplet composition kept constant and equal to its initial composition and heat
transport inside the droplet described by the conduction limit model (pure
spherically symmetric heat conduction)) and second the rapid mixing
(corresponds to infinite mass diffusion and heat conduction). Fig. 16 shows the
comparison for the two liquid phase models with the experimental data. The effect
of the two different models can be seen only in the later stages of the droplets
lifetime. As suggested in Zhang and Law 2008, since these represent the two
extreme mixing conditions, the reality lays certainly in between. Note that the
present comparison has been carried out for ambient-pressure and moderate
temperature conditions.
The original publication is available at www.springerlink.com 23
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Fig. 16 Comparison of liquid phase models with experimental arithmetic mean diameter for (a)
30% isopropanol / 70% n-nonane; (b) 70% isopropanol / 30% n-nonane
In order to determine the main physical properties controlling the evaporation in
our experiment, simulations with SPRAYSIM have been performed for n-nonane
droplets, swapping one thermophysical property at a time to that of isopropanol.
The effect of slightly different spray initial conditions at z = 5 mm was excluded
by setting the initial conditions in the computations of n-nonane equal to those of
isopropanol.
Fig. 17 N-Nonane and Isopropanol: vapor pressure and latent heat of vaporization (a) temperature
dependence; (b) evolution along the droplet trajectory
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120ExperimentRapid MixingFrozen
z [mm]
D[µ
m]
0 50 100 150 2000
20
40
60
80
100
120ExperimentRapid MixingFrozen
(a) (b)
z [mm]
p vap
[Pa]
∆hev
ap[J
/kg]
100 200
0.0E
+00
7.5E
+03
1.5E
+04
2.3E
+04
3.0E
+04
0.0E
+00
2.5E
+05
5.0E
+05
7.5E
+05
1.0E
+06
Isopropanol pvapNonane pvapIsopropanol ∆hevapNonane ∆hevap
T [K]
p vap
[Pa]
∆hev
ap[J
/kg]
300 350 400
0.0E
+00
7.5E
+04
1.5E
+05
2.3E
+05
3.0E
+05
0.0E
+00
2.5E
+05
5.0E
+05
7.5E
+05
1.0E
+06
Isopropanol pvapN-nonane pvapIsopropanol ∆hevapN-nonane ∆hevap
(a) (b)
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z [mm]
D[µ
m]
T[K
]
100 2000
20
40
60
80
100
120
300
350
400
450
500
550
600
NonaneIsopropanolNonane (∆hevap Isopropanol)Nonane (pvap Isopropanol)
Fig. 18 Diameter and temperature evolution of nonane and adpoted vapor pressure of a single
droplet with a trajectory along the centerline
It was found that the heat capacity of the liquids and the binary diffusion
coefficient have a negligible influence on the droplet diameter toward the end of
the penetration length. Fig. 17 (a) shows a comparison for both fuels of the main
physical properties found to be controlling the evaporation, namely the vapor
pressure pvap and the heat of vaporization ∆hevap. The evolution of these properties
along the droplet trajectory is shown in Fig. 17 (b). It should be noted that all
implemented thermophysical properties are taken from critically evaluated
databases (Frenkel et al. 2008; Lemmon et al. 2007) to ensure high data quality.
In Fig. 18 the distinct effect of both thermodynamic properties on the diameter
evolution and droplet temperature are shown. The vapor pressure at the same
temperature is much higher for isopropanol than it is for n-nonane (Fig. 17 a). As
expected, the normal boiling point Tnb is much lower for isopropanol
(Tnb_isopropanol=355.4 K) than it is for n-nonane (Tnb_nonane=423.9 K). In our case, as
the droplet temperature raises to an asymptotic evaporation-end temperature, the
so-called wet-bulb temperature, which is always below the boiling temperature at
ambient pressure, the n-nonane droplets heat-up to higher temperatures with
respect to isopropanol droplets, see Fig. 18. Consequently, the vapor pressure of
n-nonane droplets is above that of the colder isopropanol droplets after z = 85
mm, see Fig. 17 (b). Therefore, the evaporating mass flow from the n-nonane
The original publication is available at www.springerlink.com 25
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droplets is initially smaller with regard to the one of isopropanol droplets (with
same initial temperature), but then becomes larger (steeper dD/dz in Fig. 18) due
to the increased droplet temperature. Both droplets approach their wet-bulb
temperature at z~110 mm (Fig. 18), where the heating-up phase of the droplet
ends. In the beginning of the heating-up phase, the conductive heat flow from the
hot ambient gas onto the liquid surface is still large because the counteracting
effect of the convective vapor mass flow (Stefan flow) from the surface into the
ambient is still small (weak evaporation phase), and because the temperature
difference between the hot ambient and the liquid surface (cold droplet) is still
large. In that state, the energy transported by the conductive heat flow onto the
surface is larger than the energy required for releasing the vapor molecules away
from the liquid phase. The heating process in turn leads to an increased
evaporating mass flow and lowers the temperature difference between ambient
and liquid surface, i.e. the conductive heat flow is diminishing while the energy
required for vaporizing the raising vapor mass flow is increasing: constant latent
heat (∆hevap) times increasing vapor mass flow equals increasing vaporization
energy also called heat of evaporation. The result is a continuous decrease of
energy remaining for the liquid heating. Finally, if the initial mass of the droplet
was sufficiently large, the droplet would have reached the state where this energy
sink vanishes. Then, the heating phase would be finished and droplets would have
reached their wet-bulb temperature. This state is characterized by a balance
between the energy transported by the conductive heat flow onto the surface and
the heat of evaporation. This explanation elucidates the important role of the
latent heat [J/kg] of the liquid in the droplet evaporation process. Indeed, the
simulations exhibited that for our case: If n-nonane had the same latent heat as
isopropanol (which is roughly twice as high as that of n-nonane, Fig. 17), the n-
nonane droplet would have nearly the same overall penetration length as the
isopropanol droplet in our case, as shown in Fig. 18. But as the latent heat of n-
nonane is actually lower, the penetration length of n-nonane droplets was much
smaller than that of isopropanol droplets. In other words: The higher heat of
vaporization of isopropanol turned out to be responsible for its slower evaporation
compared to n-nonane in our case.
The original publication is available at www.springerlink.com 26
http://dx.doi.org/10.1007/s00348-011-1169-0
Conclusions
Numerical simulations and experimental measurements of evaporating sprays of
single component and binary mixtures fuels in a hot turbulent flow were
presented. N-nonane, isopropanol and their mixtures were used in the study.
The investigation was carried out in an experimental system with controlled fluid
dynamics and well defined boundary conditions. The fuel sprays, produced by
means of a calibrated droplet generator, were injected in an air flow electrically
preheated. The mean flow velocity and inlet temperature used in the experiments
were 1.5 m/s and 700 K, respectively. Particle image velocimetry was used to
determine the gaseous velocity fields. Generalized scattering imaging technique
was applied to simultaneously determine size, velocity and spatial location of the
evaporating droplets.
The spray transport and evaporation processes were computed with the
multiphase-flow simulation tool: SPRAYSIM coupled to ANSYS® CFX-12.0.
The computed gas field was validated against measurement data. Computed hot
gas flow field were then used for the computation of the spray evaporation. Initial
conditions for the spray computation were taken from experimental measurements
at z = 5 mm. The droplet temperature and initial composition was estimated by
performing computations of the spray heating-up behavior in the section before
the test track. Computed mean diameter and histograms of n-nonane, isopropanol
and their mixtures are found to be in very good agreement with the experimental
data.
With the validated numerical simulations it was then possible to investigate the
effect of turbulence, of internal mixing in the droplet and of the relative
importance of the different thermophysical properties under the given
experimental conditions. The flow was found to be weakly turbulent and the
expected small influence of the turbulence on the evaporation process was found
in the highest turbulence intensity (10%) region of the present flow. The effect of
different droplet mixing models (frozen composition or rapid mixing model) was
limited and could only be seen in the later stages of the droplet lifetime. Finally it
was shown that the latent heat of vaporization is the controlling factor responsible
for the faster evaporation of n-nonane droplets with respect to isopropanol
droplets.
The original publication is available at www.springerlink.com 27
http://dx.doi.org/10.1007/s00348-011-1169-0
Acknowledgments
The research was partially supported by the Italian Ministry of Economic Development within the
framework of the Program Agreement MiSE-CNR “Ricerca di Sistema Elettrico”. The Juwi
funding program of the German Aerospace Center is also greatly acknowledged.
The Applied Physics group at Istituto Motori – CNR in Naples wishes to thank TSI Inc. Minnesota
USA for having kindly provided the high resolution PowerView Plus CCD and the Insight 3G®
software package.
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